lmom2pwm {lmomco} | R Documentation

## L-moments to Probability-Weighted Moments

### Description

Converts the L-moments to the Probability-Weighted Moments (PWMs) given the L-moments. The conversion is linear so procedures based on L-moments are identical to those based on PWMs. The relation between L-moments and PWMs is shown with `pwm2lmom`.

### Usage

    lmom2pwm(lmom)

### Arguments

`lmom` | An L-moment object created by `lmom.ub` or similar.

### Details

PWMs are linear combinations of the L-moments and therefore contain the same statistical information of the data as the L-moments. However, the PWMs are harder to interpret as measures of probability distributions. The PWMs are included here for theoretical completeness and are not intended for use with the majority of the other functions implementing the various probability distributions. The relation between L-moments (λ_r) and PWMs (β_{r-1}) for 1 <= r <= 5 order is

λ_1 = β_0 mbox{,}

λ_2 = 2β_1 - β_0 mbox{,}

λ_3 = 6β_2 - 6β_1 + β_0 mbox{,}

λ_4 = 20β_3 - 30β_2 + 12β_1 - β_0mbox{, and}

λ_5 = 70β_4 - 140β_3 + 90β_2 - 20β_1 + β_0mbox{.}

The linearity between L-moments and PWMs means that procedures based on one are equivalent to the other. This function only accomodates the first five L-moments and PWMs. Therefore, at least five L-moments are required in the passed argument.

### Value

An R `list` is returned.

`betas` | The PWMs. Note that convention is the have a β_0, but this is placed in the first index `i=1` of the `betas` vector.
`source` | Source of the PWMs: “pwm”

### Author(s)

W.H. Asquith

### References

Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979, Probability weighted moments—Definition and relation to parameters of several distributions expressable in inverse form: Water Resources Research, vol. 15, p. 1,049–1,054.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`lmom.ub`, `pwm.ub`, `pwm2lmom`

### Examples

    pwm <- lmom2pwm(lmom.ub(c(123,34,4,654,37,78)))

    lmom2pwm(lmom.ub(rnorm(100)))

[Package lmomco version 0.92 Index]